In this non-mathematical post, I reflect on a few things. If non-mathematical posts offend you, then no one is obliging you to read.
Human beings are, by nature, social creatures. This is coming from a guy who, for most of his life, was irritated by almost any kind of noise: televisions, radios, people talking, people living, and so on (OK, I admit that to this day, screaming babies on GRT busses still end up reminding me of the exorcism scenes from Constantine, but anyway). You could almost have called me a misanthrope. I found myself always craving absolute solitude, perfect silence. The following words now bear a somewhat foreign ring, but: it felt blissful. When I was about 9 or 10 years old, it seemed like I was always absolutely productive, and this kind of lifestyle was immensely gratifying. In fact, during those years, I taught myself a great deal of material, in particular several programming languages, with almost no effort, and very little interaction with others. Today, I can only look back at this in amazement, and perhaps even a bit of disbelief. My attention span back then now seems skewed out of all proportion; I could spend over 15-20 hours straight attacking a task at hand incessantly.
Even as I started into university, there were few people to whom I spoke. As the years progressed however, and the mathematics became more advanced, I slowly began to change. I came to the realization that doing mathematics in any non-masturbatory fashion requires some pretty heavy human interaction. One cannot simply read books, Wikipedia articles, and notes in the hopes of getting anywhere. All of these are forms of media — abstractions of direct communication. If you try to read any significant amount of math alone, there will inevitably be times where you just want to phone up the (usually deceased) authors and ask them just how the hell paragraph M on page N in their book makes any sense at all. Instead of struggling like this, a much better idea is to somehow find another keen person you can talk to. Who knows, maybe you are exactly the person someone else could benefit massively from, too. I have to admit, whenever the 4-month-periodic boomerang of exams reminds me of its existence, my experience is always the same: meeting up and studying together with someone for a few hours usually enlightens me a thousand times more than scratching my head reading notes on my own all day. Solitary exploration does have its place, but you have to keep a good balance. Suffice it to say that I am extremely indebted to the various people who, without even thinking twice, I regularly pester with problems that are plaguing me. Mathematics is a social science in a different sense of the expression than you are probably accustomed to.
Now that I have talked about what an integral part of life people are, allow me to cordially contradict myself. In the theory of Lebesgue integration, we see that the integral is concerned only with how functions behave “in the large”. If two functions are the same almost everywhere, they have the same integral. I contend that to a sufficiently refined and sobered mind, it is obvious that people are almost-everywhere impermanent. This is not intended to be disrespectful, or to insult anyone I know, but merely to point out the reality that sooner or later, chances are that we’ll never see each other again. I must emphasize that I say “impermanent”, not “insignificant”. My life has been altered, for better or for worse, by many. We, as humans, are so widely and wildly varied in our interests, goals, and values that it is usually unrealistic to expect our social connections to be permanent. Friendships and relationships, however, are among the true jewels of existence, and often demonstrate to us that those lines and faces, which we foolishly assumed were inherently finite boundaries of life and happiness, were but mere aberrations, and thus we obtain a fleeting panoramic glimpse of that which lies beyond. On the other hand, individual people rarely play a role in the large; they are simply akin to the cycles that make up a complex, intricate permutation. It does not toll me psychologically to admit that I am not unique, or even quasi-unique. When it comes to human beings, the number of instances is breathtaking, and the initial and developmental conditions are comparatively narrow. We are bound to not be very “unique”; we are bound to love, like, and love again; we are doomed to watch close friendships fade away or be mutilated; we are programmed to be short-sighted, and to allow such things to preoccupy us. However, it is perhaps better to realize that everything in life happens for a reason. We will survive, and eventually, we will once again obtain that panoramic glimpse, perhaps for a greater duration this time… these are the very fibers of life.
Enjoy the break.